Question

The bottom of a right cylindrical shaped vessel made from metallic sheet is closed by a cone shaped vessel as shown in the figure. The radius of the circular base of the cylinder and radius of the circular base of the cone are each equal to 7 cm. If the height of the cylinder is 20 cm and height of cone is 3 cm, calculate the cost of milk to completely fill this vessel at the rate of Rs. 20 per litre.

Answer 1

Given that,

The radius of both cylindrical vessel and cone is $$7\ cm$$.

The height of the cylindrical vessel is $$20\ cm$$ and that of the cone is $$3\ cm$$.

The cost of one litre milk is $$Rs.\ 20$$.

To find out,

The cost of filling the vessel completely with milk.

We know that,

Volume of cylinder = $$\pi r^2h$$

$$\Rightarrow \dfrac{22}{7} \times 7 \times 7 \times 20 $$

$$\Rightarrow 3080 \ \mathrm{cm}^{3} $$

We also know that,

Volume of Cone $$=\dfrac{1}{3}\pi r^{2} h $$

$$\Rightarrow \dfrac{1}{3} \times \dfrac{22}{7} \times 7 \times 7 \times 3 $$

$$\Rightarrow 154 \ \mathrm{cm}^{3} $$

Now,

Total volume of cylindrical vessel = volume of cylinder - volume of cone

$$\Rightarrow 3080-154=2926 \ \mathrm{cm}^{3}$$

$$\therefore \ $$ total milk required to completely fill the vessel $$=2.926\ l $$ $$[1l=1000 \ \mathrm{cm^3}]$$

$$\therefore \ $$The cost of filling milk $$ =2.926 \times 20=\mathrm{Rs} .\ 58.520 $$

Hence, the cost of milk required to completely fill the vessel is $$Rs. \ 58.520$$